1−Assignment for theBMeson

Abstract

The $\pi \pi$, $\pi \omega$ scattering amplitudes in the $I=J=1\mathrm{}$ state are parameterized in terms of five parameters which are determined so as to give the $\rho$ meson position and width, the $\omega$ width, and the $B$ meson position and its $\pi \omega$ decay width under the assumption that $B$ has quantum numbers $1^{-}$. These amplitudes are then used to discuss $\pi \pi$, $\pi \omega$ production processes in terms of a simple peripheral model including $\pi$, $\omega$ exchanges. The model predicts a large ${\pi }^{+}{\pi }^{-}$ decay rate of $B$, with a cross section comparable to the experimental ${\pi }^{+}{\pi }^{-}$ resonant cross section (the $f^0$) observed at approximately the same position as the $B$ meson. On the other hand, since the $B$ is an $I=1\mathrm{}$ particle, this implies that the branching ratio of the $2{\pi }^0$ decay to that of the ${\pi }^{+}{\pi }^{-}$ decay should be small. This is incompatible with the experimentally observed large branching ratio. Within the limitations of our model, it is therefore unlikely that the $B$ meson is a $1^{-}$ particle.